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Twenty-Three Moves Suffice

After solving more than 200,000 cosets, we have been able to show that every position of Rubik's cube can be solved in 23 or fewer face turns.

The key contribution for this new result was 7.8 core-years of CPU time contributed by John Welborn and Sony Pictures Imageworks, using idle time on the render farm that was used for pictures such as Spider-Man 3 and Surf's Up.

No distance 21 positions were found in this search, despite solving a total of more than four million billion cube positions.

The same techniques for the proof of twenty-five moves were used, just on many more computers.

To prove 22 would require, using this technique, solving somewhere between 1 and 1.5 million cosets. We are investigating refinements to our techniques to reduce the CPU time required.

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Thanks

2. A suggestion from Herbert Kociemba on improving the way the coset solver worked. This suggestion simplified some of the code and lifted the "restriction" that the rubik25 paper discusses.

The amount of CPU time required to prove 20 (my ultimate goal) is still absolutely insane; it's on the order of 3500 core-years. So there's still some work to do to reduce this (or we just wait on Moore's Law).

And there's always the chance some position will actually require more than 20 moves; if I find a 21, suddenly the problem is easier.